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dc.contributor.advisorMadan, KC-
dc.contributor.advisorLucas, CA-
dc.contributor.authorKhalaf, Rehab-
dc.descriptionThis thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.en_US
dc.description.abstractThis research investigates a batch arrival queueing system with a Bernoulli scheduled vacation and random system breakdowns. It is assumed that the repair process does not start immediately after the breakdown. Consequently there maybe a delay in starting repairs. After every service completion the server may go on an optional vacation. When the original vacation is completed the server has the option to go on an extended vacation. It is assumed that the system is equipped with a stand-by server to serve the customers during the vacation period of the main server as well as during the repair process. The service times, vacation times, repair times, delay times and extended vacation times are assumed to follow different general distributions while the breakdown times and the service times of the stand-by server follow an exponential distribution. By introducing a supplementary variable we are able to obtain steady state results in an explicit closed form in terms of the probability generating functions. Some important performance measures including; the average length of the queue, the average number of customers in the system, the mean response time, and the value of the traffic intensity are presented. The professional MathCad 2001 software has been used to illustrate the numerical results in this study.en_US
dc.publisherBrunel University, School of Information Systems, Computing and Mathematics-
dc.relation.ispartofSchool of Information Systems, Computing and Mathematics-
dc.subjectBernoulli schedule vacationen_US
dc.subjectBatch arrivalsen_US
dc.subjectSupplementary variable techniqueen_US
dc.subjectMarkov processen_US
dc.subjectProbability generating functionen_US
dc.titleOn some queueing systems with server vacations, extended vacations, breakdowns, delayed repairs and stand-bysen_US
Appears in Collections:Dept of Mathematics Theses
Mathematical Sciences

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